Noreen Houlihan, whose daughter was friends with O’Riordan, signed the book with her son David.

"She was very shy, very quiet, hadn’t much confidence," she said.

"She was a lovely girl, I was crying over her yesterday. I heard it over the radio. God help her mother and her children, it’s very sad."

The tributes came after the tragic Cranberries star was found dead at a hotel in London on Monday. London Metropolitan Police have said her death is not being treated as suspicious.

Polish couple Sebastian and Michalina Buczkowski came to pay tribute to the star by signing their names. They said they had been fans of O’Riordan since they first listened to The Cranberries when they were growing up in Poland.

"I know the band from the beginning like, from the Zombies when they started," said Mr Buczkowski.

"We’re in Limerick 10 years now and we know the band as a famous band and just pay the tribute for her, that’s what we did.

"For us [she was] a famous person we should never see in real life, but in Limerick you could met them on the street."

Ms Buczkowski said: "We grew up listening to the band so very sad. We love to play and sing their songs."

"Oh she did us so proud, oh she did us so proud, she never left us down and she loved Limerick and never tired of telling us," the Limerick native said.

"Remember when she was at her height, this city was going through a dreadful, dreadful time, we had a very bad name - ’city’ - she did away with all that. You know she gave us back our pride."

Ms Sexton said it was important for her to record her sadness.

"Maybe sometime in the future her children may look at these books and realise how much we loved her mother," she said.

Limerick musician Ray Murphy said the authenticity of her voice was what made O’Riordan appeal to so many people.

"She had totally original sound that when you heard it, instantaneously, you knew who it was," he said.

"If you go back 20 odd years ago, a lot of bands, naturally, a lot of bands in Ireland were very influenced by the American sound. She didn’t think like that at all."

Mr Murphy said she was a very brave person for the way that she wrote.

"She was a very brave woman writing on certain issues," he said.

"I remember seeing Zombie on TV and just being floored by it, like, you know, the size of the sound and the power coming out of the song was incredible. You couldn’t help but be blown away by the song."

The principal of the singer’s old school, Laurel Hill Colaiste in Limerick, was one of the first to sign the book.

Aedin Ni Bhriain said the school is very proud of everything O’Riordan achieved.

She said she never forgot her roots and even asked the school choir to sing at her wedding.

"We wanted to express our sympathy to her family because it is such a loss for them and also to show our deep love for everything she did and out admiration for everything she achieved," she said.

"We are very proud of her as a past pupil and also because she was a Limerick woman who never forgot she was a Limerick woman.

"She kept the links with Limerick. We are so proud of everything she achieved."

The Government is facing fresh claims that it is failing to address spiralling health waiting list delays after a patient was told a hospital could not see him for a neurological condition until at least 2024.